CN113341728A - Anti-noise type return-to-zero neural network four-wheel mobile mechanical arm trajectory tracking control method - Google Patents

Anti-noise type return-to-zero neural network four-wheel mobile mechanical arm trajectory tracking control method Download PDF

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CN113341728A
CN113341728A CN202110700910.0A CN202110700910A CN113341728A CN 113341728 A CN113341728 A CN 113341728A CN 202110700910 A CN202110700910 A CN 202110700910A CN 113341728 A CN113341728 A CN 113341728A
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mechanical arm
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孙中波
周彦鹏
刘克平
刘永柏
王刚
唐世军
李岩
张振国
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Changchun University of Technology
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Abstract

The invention discloses a four-wheel mobile mechanical arm track tracking control method of an anti-noise return-to-zero neural network, which comprises the following steps: a. measuring the data of the wheels of the four-wheel mobile mechanical arm and the mechanical arm; b. the method comprises the following steps of (1) giving a desired track of the four-wheel moving mechanical arm; c. establishing a kinematic equation by combining the kinematic characteristics of the four-wheel mobile mechanical arm; d. obtaining a mechanical arm kinematics equation through space coordinate transformation; e. establishing an overall kinematic equation of the four-wheel mobile mechanical arm based on the mobile platform and the mechanical arm model; f. defining a vector type error function aiming at the track tracking problem; g. and obtaining a kinetic equation of the anti-noise return-to-zero neural network by combining a kinematic equation, and solving the problem of track tracking of the four-wheel mobile mechanical arm under noise disturbance. The anti-noise type return-to-zero neural network controller is designed based on the difference value between the expected track and the actual motion track as an error function, noise interference in the track tracking process of the four-wheel mobile mechanical arm is inhibited, and a track tracking task is completed.

Description

Anti-noise type return-to-zero neural network four-wheel mobile mechanical arm trajectory tracking control method
Technical Field
The invention relates to the field of mobile robots, in particular to a trajectory tracking control algorithm for a four-wheel mobile mechanical arm based on kinematics and an anti-noise return-to-zero neural network.
Background
In recent years, the manufacturing industry of China is continuously and rapidly developed, the overall scale is greatly improved, and the method plays a positive role in promoting domestic economy and world economy. The domestic manufacturing industry still dominates labor-intensive low-end manufacturing, the added value is relatively low, and the whole manufacturing industry is only a 'world factory'. With the rapid development of domestic economy and the trend of aging of population, the labor cost must be gradually increased, and the 'population dividend' of the Chinese manufacturing industry gradually disappears. In addition, the fourth industrial revolution centered on "smart manufacturing" is rolling the world. China insists on putting the focus of developing economy on physical economy, accelerates the construction of manufacturing and quality-enhancing countries, realizes the industrial upgrading of manufacturing industry, and provides the fourteenth five-year planning and 2035-year prospective target outline by the country. With the continuous advance of intelligent manufacturing, the robot changer is gradually developing. When the mobile mechanical arm works in a dynamic and unknown complex environment, the system should have complete autonomy, that is, the system should have sensing capability, planning capability, maneuvering capability, coordination capability and the like, so in the aspect of theoretical research of the mobile mechanical arm, the problems to be solved include trajectory planning, motion control, cooperative control and the like. The motion control of the mobile mechanical arm can be divided into three types of point stabilization, path following and track tracking according to the difference of control targets, wherein the track tracking control of the mobile mechanical arm is a hotspot and a difficulty of research in the current control field.
Most of the theoretical researches on the mobile mechanical arm at the present stage are based on two wheels or three wheels, the robots are based on most of dynamic modeling, the dynamic modeling of the four-wheel mobile mechanical arm is complex, and the dynamics of the mobile platform and the dynamic model of the mechanical arm need to be analyzed. The two models are difficult to integrate in one system, so most researchers adopt two control algorithms to respectively control the two subsystems, and the cooperative control of the mobile platform and the mechanical arm is difficult to realize. Therefore, the invention integrates the kinematics model of the mobile platform and the kinematics model of the mechanical arm in a system based on a world coordinate system through space coordinate transformation by establishing the kinematics model of the mobile platform and the kinematics model of the mechanical arm, and provides the four-wheel mobile mechanical arm track tracking control method of the anti-noise return-to-zero neural network, thereby realizing the track tracking control of the four-wheel mobile mechanical arm.
Disclosure of Invention
The invention discloses a four-wheel mobile mechanical arm track tracking control method of an anti-noise return-to-zero neural network, which is characterized in that a system overall kinematic equation is established based on four-wheel mobile mechanical arms under a world coordinate system, an expected track equation is designed in a reachable space range of the mobile mechanical arms, a vector type error function is defined based on a difference value between an expected track function and an actual motion track function, and a differential equation of an error function e (t) is constructed to meet the requirement
Figure BDA0003123538300000021
ψ (·) represents an activation function, and a linear activation function ψ (e (t)) ═ e (t)) is selected, whereby e (t)) ═ e (0) exp (- γ t) can be obtained, and the error function e (t) converges to 0 as time t becomes larger. The anti-noise type return-to-zero neural network dynamic model is obtained by combining the overall kinematic equation of the four-wheel mobile mechanical arm, noise interference of the four-wheel mobile mechanical arm in the track tracking process is suppressed, and noise interference of external force collision, instantaneous attenuation of power supply voltage in a control module and the like of the four-wheel mobile mechanical arm in the expected track tracking process is solved. In addition, kinematic modeling is relatively simple compared to dynamic modeling of the system. The technical scheme of the invention is as follows by combining the attached drawings of the specification:
a four-wheel mobile mechanical arm track tracking control method of an anti-noise return-to-zero neural network comprises the following specific steps:
s1: acquiring initial angle data of four wheels of a four-wheel mobile mechanical arm and initial angle data of a four-degree-of-freedom mechanical arm;
s2: according to the requirements of a designer, simultaneously giving an expected trajectory equation in the reachable space range of the four-wheel mobile mechanical arm;
s3: the kinematics equation of the four-degree-of-freedom mechanical arm under the base coordinate system is obtained through space coordinate transformation, the kinematics equation is obtained by analyzing the motion characteristics of the mobile platform, and the overall kinematics equation of the mobile mechanical arm under the world coordinate system is obtained through coordinate transformation by combining the kinematics models of the four-degree-of-freedom mechanical arm and the mobile platform.
S4: in order to solve the problem of track tracking of the mobile mechanical arm, designing a difference value between an expected track function and an actual track function as a vector error function, and designing an anti-noise return-to-zero neural network model controller;
s5: and (4) controlling the moving mechanical arm through a motor to complete a track tracking task based on the parameters solved by the neurodynamic equation in the step (4).
The specific process of step S1 is:
in the experiment, hardware parameters of the four-wheel mobile mechanical arm are required to be referred, the height of the mobile platform is measured through a meter ruler, the working range of each mechanical arm is measured under the condition of power failure, and the maximum rotating speed of each joint is consulted on a hardware official website. Wherein the parameters of each joint are as follows:
shaft 1 base Working range from +90 deg. to-90 deg Maximum speed (250 load) 320 DEG/s
Axle 2 big arm Working range of 0 DEG to +85 DEG Maximum speed (250 load) 320 DEG/s
Shaft 3 small arm Working range of-10 deg. to +95 deg Maximum speed (250 load) 320 DEG/s
Rotation of the shaft 4 Working range from +90 deg. to-90 deg Maximum speed (250 load) 320 DEG/s
The specific process of step S2 is:
the desired trajectory of the end effector of the four-wheel mobile robot arm is designed based on the measurement values in step S1 to ensure that it does not exceed the reach of the joints of the mobile robot arm. Wherein the desired trajectory function expression is as follows:
rxd＝0.2×cos(0.1×t)
ryd＝0.2×sin(0.2×t)
rzd＝0.3×ones(1,size(t,2))
the specific process of step S3 is:
s301: in order to describe the relative position and direction relationship of the links of the four-wheel mobile mechanical arm, a coordinate system needs to be established on each link according to the joint structure of the mechanical arm. Homogeneous transformation of connecting rod coordinate system { i } relative to { i-1} by using D-H joint coordinate system establishment principlei-1TiSo-called connecting rod conversion, in which the angle of rotation alpha of the shaft is designedi-1Length of connecting rod ai-1Offset distance d of connecting rodiThe joint variable thetaiAnd thus can be decomposed into sub-transformations of the coordinate system { i }, each of which depends on only one link parameter, then there are:
i-1Ti＝Rot(x,αi-1)Trans(x,ai-1)Rot(z,θi)Trans(z,di)
the transformation general formula between the connecting rods is as follows:
Figure BDA0003123538300000051
obtaining a mechanical arm kinematics equation based on a base coordinate system through coordinate transformation:
Figure BDA0003123538300000052
wherein, c1＝cos θ1，s1＝sin θ1，c23＝cos(θ2+θ3)，s23＝sin(θ2+θ3)
S302: the mobile platform selects Mecanum wheels as driving wheels, and a four-wheel full-drive mode is adopted in the aspect of power. Resolving the motion of a Mecanum wheel chassis of a mobile platform into three independent variables for description; firstly, calculating the speed of the axle center position of each wheel; calculating the speed of the roller of which the wheel is in contact with the ground according to the result of the first step; and according to the result of the second step, calculating the actual rotating speed of the wheel to obtain the inverse solution of the four-wheel omnidirectional kinematics model:
Figure BDA0003123538300000053
further, a kinematics positive solution of the four-wheel omnidirectional chassis can be deduced:
Figure BDA0003123538300000061
wherein the content of the first and second substances,
Figure BDA0003123538300000062
the direction representing the X-axis motion, i.e., the left-right direction, is defined as positive to the right,
Figure BDA0003123538300000063
the direction of motion of the Y axis, forward and backward, is defined as forward positive, ω is the angular velocity of rotation of the yaw axis, and counterclockwise positive, by the geometric center (diagonal of the rectangle) of the four wheels. v. ofω1vω2vω3vω4Representing the speed of each wheel.
S303: by adopting a transformation matrix from the base coordinate system to the world coordinate system, an overall kinematic equation of the mobile mechanical arm under the world coordinate system can be obtained:
Figure BDA0003123538300000064
differentiating the time t by the formula to obtain the following overall kinematic equation:
Figure BDA0003123538300000065
wherein, the Jacobian matrix
Figure BDA0003123538300000066
ν＝[θT,ω]T
The final formulation is the following simplified kinematic equation:
Figure BDA0003123538300000067
Figure BDA0003123538300000071
Figure BDA0003123538300000072
wherein q is [ v, θ ═ vT]TThe angle vector of the moving mechanical arm comprises the rotation angle of the wheel of the moving platform and the rotation angle of each joint of the mechanical arm.
The specific process of step S4 is:
in practical application, various types of disturbances exist in the operation process of the four-wheel mobile mechanical arm, an anti-noise return-to-zero neural network model and a relevant model thereof are provided, and in order to monitor the inverse kinematics problem solving process of the mobile mechanical arm, a vector type error function is defined:
e(t)＝zd(t)-z(t)
wherein z isd(t) and z (t) respectively denote a moving armDesired trajectory and actual running trajectory.
In order to obtain an accurate solution of time-varying inverse kinematics, each term of the error function is required to approach zero, and the anti-noise return-to-zero neural network kinetic equation is as follows:
Figure BDA0003123538300000073
wherein psi (·) represents the activation function of the neural network, simple linear activation function psi (e (t)) ═ e (t)), gamma > 0, and lambda > 0 are adjustable parameters, and the convergence rate of the system is changed. An integral term is introduced in the kinetic equation to eliminate noise.
The method comprises the following steps of combining an overall kinematic equation and an anti-noise return-to-zero neural network kinetic equation, wherein an anti-noise return-to-zero neural network model with external disturbance is as follows:
Figure BDA0003123538300000081
wherein, eta is a noise interference term, and external interference influencing the normal work of the robot always exists in the actual running process of the mobile robot. For example, a constant external force; external forces of transient decay, etc.
Figure 1 (see attached figure) shows the composition and basic principle of neurodynamics. The anti-noise return-to-zero neural network algorithm based on time derivative information, a neural network activation function and an integral term can effectively solve the time-varying inverse kinematics equation of the four-wheel mobile mechanical arm with external disturbance. The model can be regarded as a typical closed-loop control system in a classical control theory and is regarded as a controller system consisting of a generalized proportional-integral-derivative controller.
The specific process of step S5 is:
the wheel speed of the moving platform of the four-wheel moving mechanical arm and the rotation angle of each joint in the process of tracking the expected track are solved through the kinetic equation, and the obtained parameters can be applied to each motor to adjust each joint to track.
Compared with the prior art, the invention has the advantages that:
the invention provides an anti-noise return-to-zero neural network algorithm for processing the problem of track tracking of a four-wheel moving mechanical arm. The method is characterized in that the traditional control of the mobile mechanical arm needs to establish a dynamic model of the system and respectively control the mobile platform and each joint mechanical arm, however, the invention respectively carries out kinematic modeling on the mobile platform and the four-degree-of-freedom mechanical arm to avoid complex dynamic modeling, and integrates the mobile platform and the four-degree-of-freedom mechanical arm into one system through space coordinate transformation to realize the cooperative control of the mobile mechanical arm. The invention designs an anti-noise return-to-zero neural network control algorithm to solve the problem of track tracking of a four-wheel moving mechanical arm, solves the problem of control of the moving mechanical arm under the condition of external noise interference, and verifies the effectiveness of the algorithm through a simulation experiment.
Drawings
FIG. 1 is a schematic diagram of an anti-noise return-to-zero neural network model for suppressing external time-varying disturbances;
FIG. 2 is a track-following image of an end effector of a four-wheel mobile robot arm controlled based on an anti-noise return-to-zero neural network model according to the present invention;
FIG. 3 is a top view of the four-wheel mobile robot arm end effector controlled to track a desired trajectory based on the anti-noise return-to-zero neural network model according to the present invention;
FIG. 4 is an error image of the four-wheel mobile robot arm end effector controlled to track an expected trajectory based on the anti-noise return-to-zero neural network model according to the present invention;
FIG. 5 is an error change rate image of an end effector of a four-wheel mobile robot arm controlled to track an expected trajectory based on an anti-noise return-to-zero neural network model according to the present invention;
FIG. 6 is an image of the four-wheel mobile robot arm end effector tracking the angular changes of each robot arm along an expected trajectory based on the anti-noise return-to-zero neural network model according to the present invention;
FIG. 7 is an image of angular velocity changes of each arm of an end effector of a four-wheel mobile arm controlled based on an anti-noise return-to-zero neural network model to track an expected trajectory according to the present invention;
FIG. 8 is an image of the four-wheel mobile robot arm end effector controlled to track the change of the rotation angle of each wheel of an expected track based on the anti-noise return-to-zero neural network model according to the present invention;
fig. 9 is an image of the four-wheel mobile robot arm end effector controlled to track the angular velocity change of each wheel of an expected track based on the anti-noise return-to-zero neural network model.

Claims (3)

1. A four-wheel mobile mechanical arm track tracking control method of an anti-noise return-to-zero neural network is characterized by comprising the following steps:
s1: an expected track equation of the four-wheel mobile mechanical arm is given according to requirements;
s2: giving an initial rotation angle of each wheel of the four-wheel mobile mechanical arm and an initial angle of the four-degree-of-freedom mechanical arm, and measuring the length and the width of the mobile platform;
s3: constructing an overall kinematic model of the mobile platform;
s4: designing an anti-noise return-to-zero neural network model;
s5: and combining the overall kinematics equation with the neural network model to obtain the anti-noise return-to-zero neural network controller, thereby completing the track tracking task of the four-wheel mobile mechanical arm.
2. The method for controlling the trajectory tracking of the four-wheel mobile manipulator of the anti-noise return-to-zero neural network as claimed in claim 1, wherein the specific process of step S5 is as follows:
based on the kinematics characteristics of the four-wheel mobile mechanical arm, an overall kinematics model of the four-wheel mobile mechanical arm is constructed, and the specific mathematical expression is as follows:
Figure FDA0003123538290000011
wherein P is a coefficient matrix of the overall kinematic model,
Figure FDA0003123538290000012
for equations of actual trajectory with respect to time tAnd (6) differentiating.
Figure FDA0003123538290000013
The differential of the four wheels of the four-wheel moving mechanical arm and the four mechanical arm variables to the time t is shown.
According to a design formula of the anti-noise type return-to-zero neural network model, an error function of the system is as follows:
e(t)＝zd(t)-z(t)
wherein z isd(t) is the desired trajectory, and z (t) is the actual trajectory derived by the global kinematics model.
Constructing a zeroing neural network dynamic equation with an interference term, wherein the specific mathematical expression is as follows:
Figure FDA0003123538290000021
wherein gamma is more than 0, lambda is more than 0 and is an adjustable parameter,
Figure FDA0003123538290000022
in order to expect the differentiation of the track with respect to the time t, wherein eta is the noise considered in the system, the influence of exponential decay noise, linear noise, sinusoidal noise and mixed noise on the system is considered, and the four-wheel mobile mechanical arm can complete the track tracking task under the control of the model.
3. The method for controlling the trajectory tracking of the four-wheel mobile manipulator of the anti-noise type return-to-zero neural network as claimed in claim 2, wherein the noise considered in the system is as follows:
linear noise is ηLinearity＝0.1*t；
Exponentially decaying noise to ηExponential decay＝e-0.2*t；
Sinusoidal noise of ηSine wave＝sin(0.2*t)；
Mixed noise of ηMixing＝ηExponential decay+ηLinearity+ηSine wave。
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CN114721273A (en) * 2022-04-22 2022-07-08 湖南师范大学 Multi-agent formation control method of fixed time convergence zero-ization neural network
CN114721273B (en) * 2022-04-22 2024-04-12 湖南师范大学 Multi-agent formation control method for fixed-time convergence zero-change neural network
CN115107032A (en) * 2022-07-15 2022-09-27 海南大学 Pseudo-inverse-based adaptive anti-noise mobile mechanical arm motion planning method
CN115107032B (en) * 2022-07-15 2024-04-05 海南大学 Motion planning method of mobile mechanical arm based on pseudo-inverse and capable of adaptively resisting noise

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